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In the xy-plane, if line k has negative slope and passes through the
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02 Jul 2012, 02:45
02 Jul 2012, 02:45
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Question Stats:
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43%
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wrong
based on 4612
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In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?
(1) The slope of line k is -5.
(2) r > 0
(1) The slope of line k is -5.
(2) r > 0
In the xy-plane, if line k has negative slope and passes through the
[#permalink]
02 Jul 2012, 02:47
02 Jul 2012, 02:47
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Expert Reply
SOLUTION
In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?
This question can be done with graphic approach (just by drawing the lines) or with algebraic approach.
Algebraic approach:
Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line, \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)), and \(x\) is the independent variable of the function \(y\).
We are told that slope of line \(k\) is negative (\(m<0\)) and it passes through the point (-5,r): \(y=mx+b\) --> \(r=-5m+b\).
Question: is x-intercept of line \(k\) positive? x-intercep is the value of \(x\) for \(y=0\) --> \(0=mx+b\) --> is \(x=-\frac{b}{m}>0\)? As we know that \(m<0\), then the question basically becomes: is \(b>0\)?.
(1) The slope of line \(k\) is -5 --> \(m=-5<0\). We've already known that slope was negative and there is no info about \(b\), hence this statement is insufficient.
(2) \(r>0\) --> \(r=-5m+b>0\) --> \(b>5m=some \ negative \ number\), as \(m<0\) we have that \(b\) is more than some negative number (\(5m\)), hence insufficient, to say whether \(b>0\).
(1)+(2) From (1) \(m=-5\) and from (2) \(r=-5m+b>0\) --> \(r=-5m+b=25+b>0\) --> \(b>-25\). Not sufficient to say whether \(b>0\).
Answer: E.
Graphic approach:
If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.
When we take both statement together all we know is that slope is negative and that it crosses some point in II quadrant (-5, r>0) (this info is redundant as we know that if the slope of the line is negative, the line WILL intersect quadrants II). Basically we just know that the slope is negative - that's all. We can not say whether x-intercept is positive or negative from this info.
Below are two graphs with positive and negative x-intercepts. Statements that the slope=-5 and that the line crosses (-5, r>0) are satisfied.
\(y=-5x+5\):
\(y=-5x-20\):
For more on Coordinate Geometry check: https://gmatclub.com/forum/math-coordina ... 87652.html
Answer: E.
Untitled.png [ 11.06 KiB | Viewed 39546 times ]
Untitled2.png [ 4.86 KiB | Viewed 39321 times ]
In the xy-plane, if line k has negative slope and passes through the point (-5,r), is the x-intercept of line k positive?
This question can be done with graphic approach (just by drawing the lines) or with algebraic approach.
Algebraic approach:
Equation of a line in point intercept form is \(y=mx+b\), where: \(m\) is the slope of the line, \(b\) is the y-intercept of the line (the value of \(y\) for \(x=0\)), and \(x\) is the independent variable of the function \(y\).
We are told that slope of line \(k\) is negative (\(m<0\)) and it passes through the point (-5,r): \(y=mx+b\) --> \(r=-5m+b\).
Question: is x-intercept of line \(k\) positive? x-intercep is the value of \(x\) for \(y=0\) --> \(0=mx+b\) --> is \(x=-\frac{b}{m}>0\)? As we know that \(m<0\), then the question basically becomes: is \(b>0\)?.
(1) The slope of line \(k\) is -5 --> \(m=-5<0\). We've already known that slope was negative and there is no info about \(b\), hence this statement is insufficient.
(2) \(r>0\) --> \(r=-5m+b>0\) --> \(b>5m=some \ negative \ number\), as \(m<0\) we have that \(b\) is more than some negative number (\(5m\)), hence insufficient, to say whether \(b>0\).
(1)+(2) From (1) \(m=-5\) and from (2) \(r=-5m+b>0\) --> \(r=-5m+b=25+b>0\) --> \(b>-25\). Not sufficient to say whether \(b>0\).
Answer: E.
Graphic approach:
If the slope of a line is negative, the line WILL intersect quadrants II and IV. X and Y intersects of the line with negative slope have the same sign. Therefore if X and Y intersects are positive, the line intersects quadrant I; if negative, quadrant III.
When we take both statement together all we know is that slope is negative and that it crosses some point in II quadrant (-5, r>0) (this info is redundant as we know that if the slope of the line is negative, the line WILL intersect quadrants II). Basically we just know that the slope is negative - that's all. We can not say whether x-intercept is positive or negative from this info.
Below are two graphs with positive and negative x-intercepts. Statements that the slope=-5 and that the line crosses (-5, r>0) are satisfied.
\(y=-5x+5\):
\(y=-5x-20\):
For more on Coordinate Geometry check: https://gmatclub.com/forum/math-coordina ... 87652.html
Answer: E.
Attachment:
Untitled.png [ 11.06 KiB | Viewed 39546 times ]
Attachment:
Untitled2.png [ 4.86 KiB | Viewed 39321 times ]
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Re: In the xy-plane, if line k has negative slope and passes through the
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11 May 2016, 00:48
11 May 2016, 00:48
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Bunuel wrote:
In the xy-plane, if line k has negative slope and passes through the point (-5,r) , is the x-intercept of line k positive?
(1) The slope of line k is -5.
(2) r > 0
(1) The slope of line k is -5.
(2) r > 0
Diagnostic Test
Question: 39
Page: 26
Difficulty: 650
Question: 39
Page: 26
Difficulty: 650
I will not repeat the solutions above because I did the same way.
I will just repeat the most important takeaway: When slope is negative then both intercepts will have equal sign but when the slope is positive the intercepts will have opposite signs. Remember this and bully your way through these type of questions.
perhaps you can explain why most people set y = 0 to find x intercept or vice versa and doest it change target question 
"0" is not mentioned . Doesn`t "0" change the target question and why 
